Download Dispersion of the liquid crystal mixture E7 across the EM spectrum

Dispersion of the liquid crystal mixture E7 across the EM spectrum
Chan-Shan Yang1 (楊承山), Ru-Pin Pan2, a (趙如蘋) and Ci-Ling Pan1, a (潘犀靈)
1
2
Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 30013
Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan 30010
a
[email protected], [email protected]
The optical constants of liquid crystals (LCs) have been studied extensively in the past.
The refractive indices of LCs are usually modeled by the extended Cauchy equation, which is
a semi-empirical equation based on known optical constants of the material from the visible to
the infrared. The corresponding birefringence (∆n) exhibit a general decreasing trend as the
wavelength increased over this spectral range. For wavelengths much longer than the mean
resonance wavelength (λ*~250 nm), i.e., infrared and beyond, ∆n is expected to approach a
limiting but appreciable value.
In this work, we have organized the refractive indices of E7, a liquid crystal mixture
widely used for various applications, reported in the literature from the visible, near infrared,
mid-infrared to the millimeter waves together with those of our data in the millimeter and
sub-millimeter wave range measured by THz time-domain spectroscopy. This is shown in Fig.
1. The data from the visible to the mid-infrared can be fitted quite well by the Cauchy
Equation reported by previous workers. The refractive indices in the THz (sub-millimeter
wave), millimeter wave and microwave range, however, deviate significantly from the fitting
curves. Similar trends can be seen from the available birefringence data across the entire
spectrum and the fitting curves, as shown in Fig. 2. The above observations could be
qualitatively explained. It is well-known that dispersion could vary significantly near
resonances. Cyanobiphenyls, such as 5CB and 7CB, are major components of E7 and 5CB are
known to have broad absorption features near 100, 140 and 165 cm-1, i.e., ~3 to 6 THz. In
particular, there is a broad shoulder extending from the sub-THz frequencies to the absorption
band near ~ 100 cm-1 assigned to the libration of the rigid molecule around its long axis. The
far-infrared absorption spectrum of 7CB exhibits similar profiles with absorption bands near ~
100, 160 and 180 cm-1. Thus we can qualitatively understand the deviation of the THz
refractive indices of E7, because the known 3-parameter Cauchy Equation does not take into
account these far-infrared resonances.
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Δn(fitting,Ref[1])
Δn(fitting,Ref[3])
Δn(fitting,Ref[2])
Δn(data,Ref[2])
Δn(data,Ref[2])
Δn(data,Ref[2])
Δn(data,Ref[4-6])
0.44
0.40
0.36
0.32
n
Δn
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0.48
ne(fitting,Ref[1])
no(fitting,Ref[1])
ne(data,Ref[1])
no(data,Ref[1])
ne(fitting,Ref[3])
no(fitting,Ref[3])
ne(data,Ref[3])
no(data,Ref[3])
ne(data,Ref[4-6])
no(data,Ref[4-6])
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0.28
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0.16
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0.12
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10
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Wavelength (μm)
Fig. 1
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Wavelength (μm)
Fig. 2
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